Could you please mathematically describe what boundary condition you would like to have on the boundary in question. If you would like to have a the following condition:
\frac{\partial u}{\partial n} + \alpha u = g and u=h on the same boundary, this is equivalent to enforcing a non-zero Neumann condition: \frac{\partial u}{\partial n} = g - \alpha h. In general, you cannot enforce Dirichlet conditions in combination with other conditions such as Neumann conditions, see 1D Cantilever Beam problem.
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